Calculate Var(π) if π represents the outcome when a fair die is rolled.
Calculate Var(π) if π represents the outcome when a fair die is rolled.
3. A fair die is rolled twice. Let the first outcome be X and the second outcome be Y (a) (5 points) Calculate Cov(XY, X -Y) and simplify. (hint: What is Cov(aX+bY) in terms of Cov(X, Y)?) (b) (5 points) Are X Y and X -Y independent? Explain. (c) (5 points) Calculate the moment generating function Mx+y(t) of X+Y (the answer should be a function of t and can contain unsimplified sums)
b) Find Var(X) 5. A fair six sided die is rolled 10 times. Let X be the number of times the number '6' is rolled. Find P(X2) B SEIKI
In this experiment, both a fair four-sided die and a fair six-sided die are rolled (these dice both have the numbers most people would expect on them). Let Z be a random variable that represents the absolute value of their difference. For instance, if a 4 and a 1 are rolled, the corresponding value of Z is 3. (a) What is the pmf of Z? (b) Draw a graph of the cdf of Z
A fair die is rolled three times. We say that a match has occurred if the outcome of the first throw is 2, or the outcome of the second throw is 2, or the outcome of the third throw is 3. Find the probability of the event that a match occurs.
2. A fair red die and a fair blue die are rolled 2 times each. What is the probability of the product of numbers on the red die is less then the sum of numbers on the blue die? -Ive already posted this question but the answer given didn't explain how to calculate the number of successful cases. I know the total possible cases is 6*6*6*6=1296, but how do you calculate the number of successful cases?
A 20-sided fair die and an 8-sided fair die are rolled. What is the probability of rolling: exactly a 5 on the first die OR a 2 or larger on the second die? Enter your answer as a reduced fraction. ________________
2. A fair red die and a fair blue die are rolled 2 times each. What is the probability of the product of numbers on the red die is less then the sum of numbers on the blue die?
When a fair die is rolled, it has equal chance to show one of six faces, labelled 1 through 6. If it is rolled 10 times, what is the probability that there are at least three 6's?
Problem 8 A fair die is rolled 10 times. What is the probability that the rolled die will not show an even number?
(3.) A fair six-sided die is rolled repeatedly. Let R denote the random variable representing the outcome of any particular roll. The following random variables are all discrete-time Markov chains. Specify the transition probabilities for each (as a check, make sure the row sums equal 1) (a) Xn, which represents the largest number obtained by the nth roll. (b) Yn, which represents the number of sixes obtained in n rolls.